We present a weak-lensing analysis for the merging galaxy cluster, CIZA J2242.8+5301, hosting double radio relics, using three-band Subaru/Suprime-Cam imaging ($Brz$). Since the lifetime of dark matter halos colliding into clusters is longer than that of X-ray emitting gas halos, weak-lensing analysis is a powerful method to constrain a merger dynamics. Two-dimensional shear fitting using a clean background catalog suggests that the cluster undergoes a merger with a mass ratio of about 2:1. The main halo is located around the gas core in the southern region, while no concentrated gas core is associated with the northern sub halo. We find that the projected cluster mass distribution resulting from an unequal-mass merger is in excellent agreement with the curved shapes of the two radio relics and the overall X-ray morphology except for the lack of the northern gas core. The lack of a prominent radio halo enables us to constrain an upper limit of the fractional energy of magneto-hydrodynamics turbulence of $(delta B/B)^2<mathcal{O}(10^{-6})$ at a resonant wavenumber, by a balance between the acceleration time and the time after the core passage or the cooling time, with an assumption of resonant acceleration by second-order Fermi process.
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